Abstract: We consider Calderón-Zygmund operators on product domains. Under certain weak conditions on the kernel a singular integral operator can be proved to be bounded on , if its behaviour on and on certain scalar-valued and vector-valued rectangle atoms is known. Another result concerns an extension of the authors' results on -variants of Calderón-Zygmund theory [1,23] to the product-domain-setting. As an application, one obtains estimates for Fourier multipliers and pseudo-differential operators.